Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a heart given that the second card is a diamond? (Round your answer to three decimal places.)

Question

Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a heart given that the second card is a diamond? (Round your answer to three decimal places.)

Answer 1

The probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

Heart = 13/52

Diamond = 13/(52-1)

I'll let you do the calculations.

Answer 2

To find the probability that the first card is a heart given that the second card is a diamond, we need to use conditional probability. We'll approach this problem step by step.

Step 1: Determine the total number of outcomes
In a standard deck of 52 cards, each card is unique, so there are 52 possible outcomes for the first card.

Step 2: Determine the number of favorable outcomes for the first card being a heart
There are 13 hearts in a deck (1 for each rank), so the number of favorable outcomes for the first card being a heart is 13.

Step 3: Determine the total number of outcomes for the second card
After the first card is drawn without replacement, there are 51 cards remaining. Therefore, there are 51 possible outcomes for the second card.

Step 4: Determine the number of favorable outcomes for the second card being a diamond
There are 13 diamonds in a deck (1 for each rank), so the number of favorable outcomes for the second card being a diamond is 13.

Step 5: Calculate the conditional probability
The probability that the first card is a heart given that the second card is a diamond can be calculated using the formula:
P(First Card is a Heart | Second Card is a Diamond) = (Number of favorable outcomes for both events) / (Total number of outcomes for the second card)

The number of favorable outcomes for the first card being a heart and the second card being a diamond is 13 (since there are 13 hearts and 13 diamonds).

P(First Card is a Heart | Second Card is a Diamond) = 13 / 51

Calculating this expression gives us approximately 0.255 (rounded to three decimal places).

So, the probability that the first card is a heart, given that the second card is a diamond, is approximately 0.255.

Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a heart given that the second card is a diamond? (Round your answer to three decimal places.)

The probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

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To find the probability that the first card is a heart given that the second card is a diamond, we need to use conditional probability. We'll approach this problem step by step.